Both these cryptocurrencies are meant for anonymous transactions. What are the major technical differences between ShadowCash and Monero?
Monero is built on Cryptonote, which uses ring signatures (which it created in the context of cryptocurrencies) and stealth addresses. ShadowCash is built on Bitcoin, and reimplemented ring signatures (in a way that broke anonymity, see https://shnoe.wordpress.com/2016/02/11/de-anonymizing-shadowcash-and-oz-coin/). I have seen claims that they have stealth addresses, however you can see an address' balance, so it seems contradictory. That's also a difference with Monero, where you can't tell an address' balance.
Monero uses a single token. ShadowCash uses two, an anonymous one and a non-anonymous one, and can transfer between the two. This causes the anonymity set to be a fraction of what it'd otherwise be.
Monero has by all accounts had a fair launch. ShadowCash is said to have a very skewed distribution (though probably less bad than the winners of such schemes, Dash and Bytecoin).
Monero is PoW. ShadowCash is PoS (after a short period of PoW). This probably explains the previous point in large part.
One difference not mentioned by others is that ShadowCash is being developed as part of larger privacy-centric framework called Umbra:
The Shadow Project's mission is to develop free and open source software that securely enables anyone in the world to exercise their natural human rights to privacy, communication, and commerce.
It allows for sending private encrypted messages, without central authority. A decentralised Marketplace is being developed that will be part of the platform. The Marketplace is being developed closed-source and will be supposedly open-sourced under MIT licence, when ready.
ShadowCash PoW lasted 6 days and was cut off to benefit the whale group behind the project that mined the first huge % of coins. There has never been a real proof other than photoshop for their developments, and that "Umbra" is just another "hype" scheme like they did first with shadow android wallet for example, that has not worked for more than a year, shadow is a team of excuses and hype conversations, nothing real happening in there other than greed.